Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).
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Correct Answer: Option B
Explanation:
\((1 - 2x)^{6} = ^{6}C_{0}(1^{6}) + ^{6}C_{1}(1^{5})(-2x^{1}) + ^{6}C_{2}(1^{4})(-2x^{2}) + ^{6}C_{3}(1^{3})(-2x^{3}) + ^{6}C_{4}(1^{2})(-2x^{4}) + ...\)
\(\text{The coefficient of} x^{4} = 15 \times 16 = 240\)
\((1 - 2x)^{6} = ^{6}C_{0}(1^{6}) + ^{6}C_{1}(1^{5})(-2x^{1}) + ^{6}C_{2}(1^{4})(-2x^{2}) + ^{6}C_{3}(1^{3})(-2x^{3}) + ^{6}C_{4}(1^{2})(-2x^{4}) + ...\)
\(\text{The coefficient of} x^{4} = 15 \times 16 = 240\)